Augmented Dickey-Fuller Test
data: tmp[, "gdp_pc"]
Dickey-Fuller = -5.0107, Lag order = 5, p-value = 0.01
alternative hypothesis: stationary
Augmented Dickey-Fuller Test
data: tmp[, "spread"]
Dickey-Fuller = -4.9057, Lag order = 5, p-value = 0.01
alternative hypothesis: stationary
Suppose we want to model consumption as a function of income. If we assume consumption is some constant fraction of your income (according to economic theory), we could write the following model:
The residual is positive when \(\text{consumption} > \alpha + \beta \times\text{income}\). Remember, these two things are \(\approx\) when in equilibrium.
In other words, if last period’s consumption is greater than the equilibrium amount, this period’s change in consumption will be less – snapping the relationship back towards equilibrium.